Distance-based approaches to inferring phylogenetic trees

Review

•  Input: – Data from a set of genes/species

•  Output: – A phylogenetic tree that accurately

characterizes the respective lineages

Inference

•  We infer trees because we don�t really know all the species, esp. ancestors represented by internal nodes.

•  Today, we�ll discuss simple approaches for phylogenetic tree inference based on distance.

Other species trees

Darwin�s Finches

Primates

http://members.aol.com/darwinpage/trees.htm

Example gene tree

Lodish et al. (2000)

A sample tree

Reed et al. (2004)

Basic construction approaches

•  Distance –  Tree accounts for evolutionary distances

estimated from data •  Parsimony

–  Tree that requires minimum about of change to explain the data

•  Maximum likelihood –  Tree that maximizes the likelihood of the data

Details about ideal distance metrics

•  D(xi, xj) >= 0 – Distances must be non-negative

•  D(xi, xi) = 0 •  D(xi, xj) = D(xj, xi)

– symmetric •  D(xi, xj) <= D(xi, xa) + D(xa, xj)

– Additive property

Goal of distance approach

•  Given a m x m matrix, where each value is the distance between two sequences.

•  Build a tree such that distances between two leaves i and j is consistent with the matrix data.

UPGMA Method

•  Unweighted Pair Group Method using Arithmetic Averages

•  Distance is defined between two clusters Ci and Cj such that:

Basic idea

•  Dij is the average distance between pairs of taxa from each cluster

•  Algorithm: – Start with one taxa per cluster –  Iteratively pick two clusters and merge – Create a new node in the tree for the

merged cluster

More specifics

•  Place each taxon at height 0 in the tree

•  While more than two clusters: –  Determine clusters with smallest dij –  Merge clusters into a new one Ck –  Make a new node k at height dij/2 –  Replace Ci and Cj with Ck –  Recompute distance of Ck to other clusters

•  Hook in the two remaining clusters to the root with height calculated as above.

Updating distances

•  Distance between Ck and Cl defined as:

In-class example

•  Consider the following symmetric matrix:

A B C D E A 0 5 3 8 10 B 5 0 5 8 10 C 3 5 0 8 10 D 8 8 8 0 1 E 10 10 10 1 0

λ UPGMA visually

Molecular clocks

•  A molecular clock assumption is divergence is uniform and equal across all branches of the tree

•  Seldom (never?) true in practice

•  If it is true, these data are called ultrametric.

Neighbor joining

•  Does not assume a molecular clock, but does assume additively –  Distance between a pair of leaves is sum of edges between

them

•  Constructs an unrooted tree iteratively, just like UPGMA

•  Two differences: –  How subtrees selected –  How distances are updated

•  Root can be added via inclusion of an �outgroup�

Basics

•  NJ is a greedy algorithm that starts with a center star tree (all taxa connected to a single root)

•  Criterion for merging is key: identifies topological neighbors using math that is correct for all additive distance matrices.

•  Once merged, the two taxa are treated as a single taxon.

λ Reconstructing a 3 leaved tree

Caveats

•  Matrix is updated iteratively after merge.

•  Produces unrooted trees; need an outgroup for a rooted version

•  Always gives the true tree if distances are additive (may not with noise)

λ Four-point condition

λ Pairwise distances are additive if and only if for every set of four leaves i,j,k,l, two of the following three sums are equal and larger than the third:

- Dij + Dkl - Dik + Djl - Dil + Djk

λ Example

• A

• B

• C

• D

• 0.1

• 0.1

• 0.1

• 0.4 • 0.4

• Neighbor-joining will find the correct tree here

One more thing

•  There are an assortment of formats for trees as there is with DNA sequence data.

•  Newick format indicated in the text is one of the more common ones (like FASTA is for sequences) – Ex: ((A,B),(C,D))

Why compute more distances?

•  The most crucial piece of NJ is computing a new matrix using the previously mentioned equations.

•  This allows us to choose the smallest one greedily, in something called the �4-point condition.�

•  UPGMA is a simpler form of NJ that is correct when distance between all taxa and the root is the same. –  This seems true but rarely holds up in observed DNA

sequence data

Calculating distances

•  Saitou and Nei (1987)

SARS

•  The genome of SARS was sequenced by a Canadian group in April 2003

•  29,751bp, single stranded RNA sequence

•  Has 5-6 genes in the typical structure of a coronavirus –  One of the causes of the common cold

Where did SARS come from?

Himalayan palm civet

Neighbor joining can also be used to study epidemiology

Date of origin

Finishing up

•  Build a NJ tree for the matrix earlier:

A B C D E A 0 5 3 8 10 B 5 0 5 8 10 C 3 5 0 8 10 D 8 8 8 0 1 E 10 10 10 1 0